Question

Domain of the function \( f(x) = \frac{1{(x-2)(x-5)} \) is:}

• A. \( (-\infty, 2) \cup (5, \infty) \)
• B. \( (-\infty, 3] \cup (5, \infty) \)
• C. \( (-\infty, 3) \cup (5, \infty) \)
• D. \( (-\infty, 2] \cup [5, \infty) \)

Hint:

For rational functions, remember to exclude values that make the denominator zero as they are not in the domain.

Answer 1

The Correct Option is A

The given function is: \[ f(x) = \frac{1}{(x-2)(x-5)} \] For the function to be defined, the denominator must not be zero. So, we solve: \[ (x-2)(x-5) \neq 0 \] This implies: \[ x \neq 2 \quad \text{and} \quad x \neq 5 \] Thus, the domain of the function is all real numbers except \( x = 2 \) and \( x = 5 \). The domain is: \[ (-\infty, 2) \cup (5, \infty) \]